Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int(input())
lst = [i*(i+1)//2 for i in range(1, 1 + int((2*n)**0.5))]
high = len(lst)-1
low = 0
flag = False

if n/2 in lst:
    flag = True
else:
    while low < high:
        if lst[low] + lst[high] == n:
            flag = True
            break
        elif lst[low] + lst[high] > n:
            high -= 1
        else:
            low += 1

print('YES' if flag else 'NO')